Introduction to the Euler Number used in fluid mechanics
The Euler Number is a dimensionless value used for analyzing fluid flow dynamics problems where the pressure difference between two points is important. The Euler Number can be interpreted as a measure of the ratio of the pressure forces to the inertial forces.
The Euler Number can be expressed as
Eu = p / (ρ v2) (1)
Eu = Euler number
p = pressure (Pa)
ρ = density (kg/m3)
v = fluid flow velocity (m/s)
The pressure difference is often used
Eu = dp / (ρ v2) (2)
dp = differential pressure (Pa)
- Note! - a perfect frictionless flow corresponds to that the Euler number equals 1
The combination below is called the pressure coefficient
pressure coefficient = dp / (1/2 ρ v2) (3)
A special version of the Euler Number is in general referred to as the Cavitation Number.